August 11, 2025

A Review on Semi-Analytic Methods for Solving Partial Differential Equations

Puntos clave

Semi-analytic methods provide effective alternatives for obtaining approximate solutions to PDEs, addressing the rarity of exact solutions.
Three key methods highlighted are the Adomian Decomposition Method, Homotopy Analysis Method, and Laplace Decomposition Method, each with distinct principles.
Example applications illustrate the principles of these methods, showcasing their relevance and effectiveness in solving complex equations.
Understanding these methods may enhance problem-solving techniques in various fields involving PDEs, indicating potential for broader applications.

Resumen

Partial Differential Equations (PDEs) play a crucial role in the modeling of various physical phenomena. Exact solutions to PDEs are rare, especially for nonlinear equations. Semi-analytic methods such as the Adomian Decomposition Method (ADM), the Homotopy Analysis Method (HAM), and the Laplace Adomian Decomposition Method (LADM) provide effective alternatives for approximate analytical solutions. This review discusses the principles and methodologies of these three methods in detail and demonstrates each with an illustrative example. MSC 2010: 47H08, 47H09, Keywords: Adomian Decomposition Method, Homotopy Analysis Method, Laplace Decomposition Method.

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